The function f is defined by f x = 4 x + k x - 1 , where k is

Question

The function f is defined by f x = 4 x + k x - 1 , where k is a constant, and f 5 = 32 . What is the value of f 10 ?

Accepted Answer

The correct answer is 67 . It&rsquo;s given that f 5 = 32 . Therefore, for the given function f , when x = 5 , f x = 32 . Substituting 5 for x and 32 for f x in the given function f x = 4 x + k x - 1 yields 32 = 4 5 + k 5 - 1 , or 32 = 20 + 4 k . Subtracting 20 from each side of this equation yields 12 = 4 k . Dividing each side of this equation by 4 yields k = 3 . Substituting 3 for k in the given function f x = 4 x + k x - 1 yields f x = 4 x + 3 x - 1 , which is equivalent to f x = 4 x + 3 x - 3 , or f x = 7 x - 3 . Substituting 10 for x into this equation yields f 10 = 7 10 - 3 , or f 10 = 67 . Therefore, the value of f 10 is 67 .

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